Unformatted text preview: determine the most e³cient way to combine these legs into ²ight schedules. The starting time for ²ight i is a i and the ±nishing time is b i . The plane requires r ij hours to return from the destination of ²ight leg i to the start (origin) point of ²ight leg j . Suggest a way to solve this problem using ²ow. 3. [6.40] Given a directed graph G = ( N, A ) with upper bounds on the ²ow u ij which are integer, and nodes s, t ∈ N , we know that there is a max ²ow from s to t that is integer. Suppose that instead, a “helpful” friend gives us a max ²ow x ′ ij where some of the ²ows are noninteger. Show how to convert this ²ow into an integer maximum ²ow. The running time of your algorithm should be O ( mf ) wher m is the number of arcs and f is the number of arcs with fractional (noninteger) ²ow on them. Hint: Send ²ows along cycles....
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This note was uploaded on 01/31/2011 for the course AMS 546 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.
- Fall '08